Nicolas ChristouUCLA Department of Statistics

Demonstration and Assessment of the Statistics OnlineComputational Resource (SOCR)

Joint work with:

Ivo Dinov (Director, Faculty)

Juana Sanchez (Faculty)

University of CyprusDepartment of Statistics

14 June 2006

Nicolas ChristouUCLA Department of Statistics

Demonstration and Assessment of the Statistics OnlineComputational Resource (SOCR)

Joint work with:

Ivo Dinov (Director, Faculty)

Juana Sanchez (Faculty)

University of CyprusDepartment of Mathematics and Statistics

14 June 2006

Outline

• What is SOCR?

• SOCR capabilities

• Research

• Future growth

What is SOCR? (not SOCCER!)

• Statistics Online Computational Resource (SOCR):It is a collection of interactive applets and computa-tional / graphing tools (2001 - Present).

• People: Ivo Dinov (Director and Faculty), JuanaSancez (Faculty), graduate students (Annie Che),programmers (Jenny Cui), and many others.

• Goal: To provide educators, students, and develop-ers a set of interactive tools in the teaching and re-search of probability and statistics at all levels.

• Funding: NSF grant (since 2005), OID (UCLA)

• Access SOCR: It is available online at

http://socr.stat.ucla.edu

and its code can be downloaded at

http://socr.stat.ucla.edu/htmls/SOCR_Download.html

Capabilities of SOCR

• There are 6 major components of SOCR:

– Distributions

– Experiments

– Analyses

– Games

– Modeler

– Charts

Distributions

• Binomial distribution

• Normal distribution

• Normal Approximation to binomial

• χ2 distribution

• Conclusion

X ∼ N(10, 3)

X ∼ Binomial(15, 0.3)

• Conclusion

X ∼ N(10, 3)

X ∼ B(15, 0.3)

Experiments

• Birthday experiment

• Let’s make a deal (Monty Hall) experiment

• Die coin experiment

• Confidence interval experiment

A die is rolled and the number observed X is recorded.Then a coin is tossed number of times equal to thevalue of X. For example if X = 2 then the coin istossed twice, etc. Let Y be the number of heads ob-served. Note: Assume that the die and the coin arefair.

a. Construct the joint probability distribution of Xand Y .

b. Find the conditional expected value of Y givenX = 5.

c. Find the conditional variance of Y given X = 5.

d. Find the expected value of Y .

e. Find the standard deviation of Y .

f. Graph the probability distribution of Y .

g. Use SOCR to graph and print the empirical dis-tribution of Y when the experiment is performed

i. n=1000 times.

ii. n=10000 times.

h. Compare the theoretical mean and standard de-viation of Y (parts (d) and (e)) with the empiricalmean and standard deviation found in part (g).

Die Coin Experiment

A die is rolled and the number observed X is recorded.Then a coin is tossed number of times equal to thevalue of X. For example if X = 2 then the coin istossed twice, etc. Let Y be the number of heads ob-served. Note: Assume that the die and the coin arefair.

a. Construct the joint probability distribution of Xand Y .

b. Find the conditional expected value of Y givenX = 5.

c. Find the conditional variance of Y given X = 5.

d. Find the expected value of Y .

e. Find the standard deviation of Y .

f. Graph the probability distribution of Y .

g. Use SOCR to graph and print the empirical dis-tribution of Y when the experiment is performed

i. n=1000 times.

ii. n=10000 times.

h. Compare the theoretical mean and standard de-viation of Y (parts (d) and (e)) with the empiricalmean and standard deviation found in part (g).

Analyses

• One sample t test

• Two sample t test

• Simple regression

• Multiple regression

Modeler

• Exponential fit

• Normal fit

• Poisson fit

• Mixture fit

Research

• Preliminary assessment of SOCR:

- SOCR was tested on 3 undergraduate courses atUCLA Department of Statistics (Dinov, Sanchez,Christou).

- Results:

∗ Students exposed to SOCR generally performedbetter compared to those not.

∗ Exit surveys (end of the courses) indicated highsatisfaction and interest in SOCR.

∗ More testing should be performed to validatethe effectiveness of SOCR tools.

– Next 3 tables show some quantitative results ofstudents performance using SOCR (control vs.treatment).

Table 1: Quantitative Results measuring student learning in the two groups of

Dinov’s Stat 13 courses

Group High Low Median MeanStandard

DeviationStatistics

Control 100 53 84.33 83.9 10Midterm

Treatment 100 58 88 86 10

to = 1.37

t(169)

p=0.089

Control 100 42 83 81.2 13Final

Treatment 99 35 87 83.8 12

to = 1.34

t(169)

p=0.093

Control 96.89 53.6 86.82 84.57 9.1Overall

PerformanceTreatment 98.05 42.32 88.26 86.68 9.9

to = 1.448

t(169)

p=0.075

Table 2: Quantitative Results measuring student learning in the two groups of

Sanchez’s Stat 100A courses

Table 3: Quantitative Results measuring student learning in the two groups of

Christou's Stat 100A course

Group High Low Median MeanStandard

DeviationStatistics

Control 34 17.5 26.5 26.19 4.65Midterm

Treatment 33 17.5 28.5 27.08 4.25

to = 0.63t(38) p>0.2

Control 19.74 4.69 16.92 15.76 4.44Homework

Treatment 19.07 13.39 16.41 16.41 1.73

to = 0.64 t(16) p>0.2

Control 37.2 18.4 29.4 28.48 5.31Final

Treatment 36.9 22.5 29.40 29.23 4.30

to=0.49 t(38)

p>0.2

Control 90.55 43.19 71.22 70.45 12.24Overall

Performance Treatment 84.89 58.42 72.44 72.73 8.08

to=0.71 t(38)

p>0.2

Group High Low Median MeanStandard

DeviationStatistics

Control 96 41 70 72.61 16.84Quiz1

Treatment 100 58 93 87.67 14.72

to = 2.644

t(42)

p=0.0058

Control 100 32 73 72.61 16.78Quiz2

Treatment 100 58 89 84.11 13.25

to = 2.063

t(42)

p<0.0227

Control 100 40 89 85.74 13.64Exam1

Treatment 100 47 96 89.56 16.62

to=0.7617

t(42)

p=0.225

Control 100 36 80 80.23 15.98Exam2

Treatment 100 68 88 87.22 11.09

to=1.342

t(42)

p= 0.0935

Control 100 46 82 82.45 14.13Exam3

Treatment 100 60 88 83.78 13.66

to=0.2725

t(42)

p=0.3933

Control 94.31 44.93 80.09 80.23 11.87Overall

Performance Treatment 96.26 60.65 90.59 86.76 11.06

to=1.606

t(42)

p=0.058

Table 1: Quantitative Results measuring student learning in the two groups of

Dinov’s Stat 13 courses

Group High Low Median MeanStandard

DeviationStatistics

Control 100 53 84.33 83.9 10Midterm

Treatment 100 58 88 86 10

to = 1.37

t(169)

p=0.089

Control 100 42 83 81.2 13Final

Treatment 99 35 87 83.8 12

to = 1.34

t(169)

p=0.093

Control 96.89 53.6 86.82 84.57 9.1Overall

PerformanceTreatment 98.05 42.32 88.26 86.68 9.9

to = 1.448

t(169)

p=0.075

Table 2: Quantitative Results measuring student learning in the two groups of

Sanchez’s Stat 100A courses

Table 3: Quantitative Results measuring student learning in the two groups of

Christou's Stat 100A course

Group High Low Median MeanStandard

DeviationStatistics

Control 34 17.5 26.5 26.19 4.65Midterm

Treatment 33 17.5 28.5 27.08 4.25

to = 0.63t(38) p>0.2

Control 19.74 4.69 16.92 15.76 4.44Homework

Treatment 19.07 13.39 16.41 16.41 1.73

to = 0.64 t(16) p>0.2

Control 37.2 18.4 29.4 28.48 5.31Final

Treatment 36.9 22.5 29.40 29.23 4.30

to=0.49 t(38)

p>0.2

Control 90.55 43.19 71.22 70.45 12.24Overall

Performance Treatment 84.89 58.42 72.44 72.73 8.08

to=0.71 t(38)

p>0.2

Group High Low Median MeanStandard

DeviationStatistics

Control 96 41 70 72.61 16.84Quiz1

Treatment 100 58 93 87.67 14.72

to = 2.644

t(42)

p=0.0058

Control 100 32 73 72.61 16.78Quiz2

Treatment 100 58 89 84.11 13.25

to = 2.063

t(42)

p<0.0227

Control 100 40 89 85.74 13.64Exam1

Treatment 100 47 96 89.56 16.62

to=0.7617

t(42)

p=0.225

Control 100 36 80 80.23 15.98Exam2

Treatment 100 68 88 87.22 11.09

to=1.342

t(42)

p= 0.0935

Control 100 46 82 82.45 14.13Exam3

Treatment 100 60 88 83.78 13.66

to=0.2725

t(42)

p=0.3933

Control 94.31 44.93 80.09 80.23 11.87Overall

Performance Treatment 96.26 60.65 90.59 86.76 11.06

to=1.606

t(42)

p=0.058

Table 1: Quantitative Results measuring student learning in the two groups of

Dinov’s Stat 13 courses

Group High Low Median MeanStandard

DeviationStatistics

Control 100 53 84.33 83.9 10Midterm

Treatment 100 58 88 86 10

to = 1.37

t(169)

p=0.089

Control 100 42 83 81.2 13Final

Treatment 99 35 87 83.8 12

to = 1.34

t(169)

p=0.093

Control 96.89 53.6 86.82 84.57 9.1Overall

PerformanceTreatment 98.05 42.32 88.26 86.68 9.9

to = 1.448

t(169)

p=0.075

Table 2: Quantitative Results measuring student learning in the two groups of

Sanchez’s Stat 100A courses

Table 3: Quantitative Results measuring student learning in the two groups of

Christou's Stat 100A course

Group High Low Median MeanStandard

DeviationStatistics

Control 34 17.5 26.5 26.19 4.65Midterm

Treatment 33 17.5 28.5 27.08 4.25

to = 0.63t(38) p>0.2

Control 19.74 4.69 16.92 15.76 4.44Homework

Treatment 19.07 13.39 16.41 16.41 1.73

to = 0.64 t(16) p>0.2

Control 37.2 18.4 29.4 28.48 5.31Final

Treatment 36.9 22.5 29.40 29.23 4.30

to=0.49 t(38)

p>0.2

Control 90.55 43.19 71.22 70.45 12.24Overall

Performance Treatment 84.89 58.42 72.44 72.73 8.08

to=0.71 t(38)

p>0.2

Group High Low Median MeanStandard

DeviationStatistics

Control 96 41 70 72.61 16.84Quiz1

Treatment 100 58 93 87.67 14.72

to = 2.644

t(42)

p=0.0058

Control 100 32 73 72.61 16.78Quiz2

Treatment 100 58 89 84.11 13.25

to = 2.063

t(42)

p<0.0227

Control 100 40 89 85.74 13.64Exam1

Treatment 100 47 96 89.56 16.62

to=0.7617

t(42)

p=0.225

Control 100 36 80 80.23 15.98Exam2

Treatment 100 68 88 87.22 11.09

to=1.342

t(42)

p= 0.0935

Control 100 46 82 82.45 14.13Exam3

Treatment 100 60 88 83.78 13.66

to=0.2725

t(42)

p=0.3933

Control 94.31 44.93 80.09 80.23 11.87Overall

Performance Treatment 96.26 60.65 90.59 86.76 11.06

to=1.606

t(42)

p=0.058

Future growth

• Possibility of future research on the incorporation ofSOCR in the teaching of statistics (high school andcollege) and the effect of a combination of SOCR asan enhancement tool to traditional teaching.

• Internationalization of SOCR:

– Currently information about SOCR can vaguelytranslated into other languages using web-basedresource.

– The possibility of expanding SOCR into otherlanguages (e.g. Greek), including Java applets.

• Software enhancement based on user-feedbacks andfurther developments.

Multilingual Support

• English (default)

• German

• Spanish

• French

• Italian

• Portuguese

• Japanese

• Korean

• Chinese

• Traditional Chinese

• Russian

• Dutch

• French

• Greek

Acknowledgments

This is joint work with

Ivo Dinov (Director)

Annie Che

Jenny Cui

Juana Sanchez

Thank you!